The present invention relates to the display of and interaction with multivariate data.
While univariate data (i.e., pairs of numbers) can be displayed readily in an x-y coordinate system on a plotter or a computer screen, methods for the display multivariate data are not as immediately obvious. For bivariate data, graphics research has long been developing true 3-dimensional (3-D) interaction devices (see, e.g., I. Sutherland "The Ultimate Display" Proc IFIP 65 1965, pp 506-508); however, it is only over the past decade that high-performance 3-D graphics workstations have been coupled with commercially available 3-D devices, e.g., polarized liquid-crystal shutters for stereo viewing, head-mounted displays, and a so-called DataGlove device (see T. Zimmerman et al., "A Hand Gesture Interface Device", Proc. CHI+GI 1987, pp. 189-192.)
In a variety of fields, e.g., science, engineering, economics, demographics, business, and finance, there are applications in which it is important to explore and manipulate four- and higher.-dimensional data in the form, e.g., of functions of three or more variables. In such applications, data can be represented by points in (Euclidean) n-dimensional space. The position of a point is then specified with n coordinates, each of which determines its position relative to one of n (mutually perpendicular) axes. In some cases, the multivariate data being presented has a familiar 3-D interpretation; e.g., as described by M Ouh-young et al., "Force Display Performs Better than Visual Display in a Simple 6-D Docking Task", Proc. IEEE Robotics and Automation Conf., 1989, pp. 1462-1466, users may explore a 6-dimensional space to find the energy minimum of positioning and orienting a rigid object in 3-space operated on by forces and torques. The user sees a representation of the forces and torques as vectors of Varying length or actually feels them through force-feedback manipulators. Another approach is described by S. Bly in "Communicating with Sound" (W. Buxton, moderator), CHI '85 Proceedings (ACM), 1985, pp. 115-119, where reference is made to a demonstration showing that users have the ability to distinguish between multivariate data presented sonically by varying seven characteristics of a musical note: pitch, volume, duration, attack envelope, wave shape, and the addition of fifth and ninth harmonics. Typically, however, in the presentation of abstract multivariate data, nonvisual properties are mapped to visual properties, e.g., position, color, and texture, that can be represented in a display. One possibility is to generalize 3-D modeling transformations and viewing projections to higher dimensions; see, e.g., M. Noll, "A Computer Technique for Displaying n-Dimensional Hyperobjects" CACM 10:8, 1967 pp. 469-473. However, although systems based on these concepts are useful research tools, an intuitive understanding of the resulting displays is often difficult to acquire.
One common approach to reducing the complexity of a multivariate function is to hold one or more of its independent variables constant. Each constant corresponds to taking an infinitely thin slice of the space perpendicular to the constant variable's axis, thereby reducing the space's dimensions. For example, if the dimension is reduced to 3, the resulting slice is a 3-D height field and represents a function of two variables that can be manipulated and displayed using a conventional 3-D graphics system.
Ostensibly, this simplification is at the expense of dimensions "sliced away" by holding variables constant, and it is a purpose of the invention to "add back" such dimensions in a controlled fashion as described in the following.